# 8.8.3.46 IfcTriangulatedFaceSet

AbRV ⓘ
RV ⓘ

## 8.8.3.46.1 Semantic definition

The IfcTriangulatedFaceSet is a tessellated face set with all faces being bound by triangles. The faces are constructed by implicit polylines defined by three Cartesian points. Depending on the value of the inherited attribute Closed the instance of IfcTriangulatedFaceSet represents:

• if TRUE, a boundary representation (or B-rep);
• if FALSE, a face based surface representation.

The coordinates of each point are provided by a one-based index into an ordered list of Cartesian points provided by the two-dimensional list CoordIndex, where

• the first dimension of the two-dimensional list addresses the list of triangular faces;
• the second dimension of the two-dimensional list provides exactly three indices. Each index points to a Cartesian point being a vertex of the triangle.

Depending on the provision of PnIndex the indices point either directly into the IfcCartesianPointList3D referenced by Coordinates defined at the supertype IfcTessellatedFaceSet, or they point into the PnIndex where the integer values at that position provides the location of the coordinate values within the IfcCartesianPointList3D. See Figure 8.8.3.46.A for the handling of point index.

See Figure 8.8.3.46.B for using the IfcTriangulatedFaceSet without (as default) and with using the PnIndex.

Optionally normals can be provided. Only normals per vector are supported allowing for visually curved triangles when the three normals of the corresponding three vertices of a triangle are not co-linear to the normal of the triangular face. If they are identical, normals shall be omitted.

Normals are provided by the two-dimensional list Normals, where

• the first dimension of the two-dimensional list addresses the corresponding list of vertex indices of the triangular faces;
• the second dimension of the two-dimensional list provides exactly three real values to determine the direction of the normal at this vertex of the triangle.

The indices in the CoordIndex point into the list of Normals. The indices of CoordIndex are applied to both points, either directly directly, or via the PnIndex and normals. See Figure 8.8.3.46.C for handling of normals.

Figure 8.8.3.46.D shows the use of IfcTriangulatedFaceSet without annotation. The diagram of the IfcTriangulatedFaceSet represents the indices and the ordered list into which the indices point. The index starts with 1 (indexed as 1 to N), if the greatest index in CoordIndex in N, then the IfcCartesianPointList shall have N lists of 3:3 coordinates.

Figure 8.8.3.46.D shows an IfcTriangulatedFaceSet represented by:

CoordIndex:
((1,6,5), (1,2,6), (6,2,7), (7,2,3), (7,8,6), (6,8,5), (5,8,1), (1,8,4), (4,2,1), (2,4,3), (4,8,7), (7,3,4))

IfcCartesianPointList3D:
((0.,0.,0.), (1.,0.,0.), (1.,1.,0.), (0.,1.,0.), (0.,0.,2.), (1.,0.,2.), (1.,1.,2.), (0.,1.,2.))


Informal Propositions:

1. If Closed = TRUE, the same topological constraints as imposed by an faceted boundary representation shall be safisfied. In particular:
• each face shall be unique;
• each edge shall be used by exactly two boundaries of faces;
• the topological normal at each point on the boundary of the triangulated face set shall point away from the material of the solid.

## 8.8.3.46.5 Formal representation

ENTITY IfcTriangulatedFaceSet
SUPERTYPE OF (ONEOF
(IfcTriangulatedIrregularNetwork))
SUBTYPE OF (IfcTessellatedFaceSet);
Normals : OPTIONAL LIST [1:?] OF LIST [3:3] OF IfcParameterValue;
Closed : OPTIONAL IfcBoolean;
CoordIndex : LIST [1:?] OF LIST [3:3] OF IfcPositiveInteger;
PnIndex : OPTIONAL LIST [1:?] OF IfcPositiveInteger;
DERIVE
NumberOfTriangles : IfcInteger := SIZEOF(CoordIndex);
END_ENTITY;